I7>>=Odd +(I)  1Courier NewTimes New Roman1Courier New1Courier NewTimes New RomanTimes New Roman1Courier New1Courier New1Courier New1Courier NewX| VX| VX| VX| V ?/ <```@@@?~~~~~ԱޱޱԱ޿޿ph (((Pdd{  d< p {2 ہ? خ7@NL +,|D@Mkpl*>j@*???@@@@@@033333??@^ߛOw?̌???98Ic@VН@@?@ @@@Їu_?c*w?@?@?@@dddddddddddddddddddddddddddddddddddddddd 2??h!@$$$h!@???????!!!!!!!!!8!(!x!!G a!r = a; 0.000000 <= t <= 6.283185$0.000000000000000;6.283185307179586PPP 2 2??@$$$@???????@?   ! " # $ % H R hN Z dZ $&"-b*(sqrt(a^2-b^2-x^2)/sqrt(abs(a^2-b^2-x^2)))Ly = b*(sqrt(a^2-b^2-x^2)/sqrt(abs(a^2-b^2-x^2))); 0.000000 <= x <= 5.000000$0.000000000000000;5.0000000000000002???$$$*$\m@?????? !!!!!!!&"88"x;":#;#:#00sqrt(a^2-b^2)bseg (0,0) to (sqrt(a^2-b^2),b)2???$$$*$\m@??????& ' ( ) * + - >#\?#T"0@#tD#d@#0-asqrt(a^2-b^2)b seg (0,-a) to (sqrt(a^2-b^2),b)2???$$$* ףp= @sDa@?????? !!!!!!!\"""`F#F#F#00sqrt(a^2-(b+d)^2)b+d%seg (0,0) to (sqrt(a^2-(b+d)^2),b+d)2??h!@$$$h!h!????????. /  0 1 2 3 4 "x""lJ.HM###ha*sqrt(arcsin((b+d)/a)-t)/sqrt(abs(arcsin((b+d)/a)-t))*sqrt(t-arcsin((b)/a))/sqrt(abs(t-arcsin((b)/a)))r = a*sqrt(arcsin((b+d)/a)-t)/sqrt(abs(arcsin((b+d)/a)-t))*sqrt(t-arcsin((b)/a))/sqrt(abs(t-arcsin((b)/a))); -1.570796 <= t <= 1.570796%-1.570796326794896;1.5707963267948962??h!@$$$h!h!???????? !!!!! !$! )) ) 4)`))ha*sqrt(t-arcsin((b+d)/a))/sqrt(abs(arcsin((b+d)/a)-t))*sqrt(arcsin((b)/a)-t)/sqrt(abs(t-arcsin((b)/a)))r = a*sqrt(t-arcsin((b+d)/a))/sqrt(abs(arcsin((b+d)/a)-t))*sqrt(arcsin((b)/a)-t)/sqrt(abs(t-arcsin((b)/a))); -1.570796 <= t <= 1.570796%-1.570796326794896;1.5707963267948962???$$$@sDa@( ףp= ?????? 5 $6 (7 ,8 09 4: 8; )/|/)*<)0-asqrt(a^2-(b+d)^2)b+d&seg (0,-a) to (sqrt(a^2-(b+d)^2),b+d)2???$$$*$\m@?????? (!,!0!4!8! H? L@ PA TB )00)10:0R0Vcos(t)*sqrt(arctan((b+a)/sqrt(a^2-b^2))-t)/sqrt(abs((arctan((b+a)/sqrt(a^2-b^2))-t))) (sin(t)-a)(x,y) = (cos(t)*sqrt(arctan((b+a)/sqrt(a^2-b^2))-t)/sqrt(abs((arctan((b+a)/sqrt(a^2-b^2))-t))),(sin(t)-a)); 0.000000 <= t <= 1.570796$0.000000000000000;1.570796326794897xyz@QQ?JXT@@@@@?@@@@@@@@@@@@@@@@@@@@@@RW$RW$RW$L = 2a sin (Psi)!"ERe@29@8fhTimes New Roman!Psi2a sin (Psi)(arctan((b+a)/sqrt(a^2-b^2))-t)/sqrt(abs((ar8E?^A?ո;LpDu=Times New Roman!r = L cos(Psi)\L\YA!=@@4ackgrounNVA*ֺhf?pߪV`ݺTimes New Romanl!ds = a(2 dPsi)\L\YA!m0@4ackgrounm@> h@1' nۈ?Times New Roman$!a^2 = (L cos(Psi))^2 + (a - L sin(Psi))^2-b^2))-t)/sqrt(abs>;4> h@ej΍ܘN>Times New Roman!"Proof" Surface area from (0,-a) to to chord = Pi*L^2 = AwT@1f)@tvbX@Tíz@Times New Roman r = a; 0.000000 <= t <= 6.283185XUi@YCc}7.٭@1Courier New L!y = b*(sqrt(a^2-b^2-x^2)/sqrt(abs(a^2-b^2-x^2))); 0.000000 <XUi@YCc}S @1Courier New !seg (0,0) to (sqrt(a^2-b^2),b)a)XUi@YCc}Z[Tk@1Courier New !seg (0,-a) to (sqrt(a^2-b^2),b)a)XUi@YCc}0QWʆ@1Courier New t!seg (0,0) to (sqrt(a^2-(b+d)^2),b+d)XUi@YCc}ƅXR?1Courier New ,!r = a*sqrt(arcsin((b+d)/a)-t)/sqrt(abs(arcsin((b+d)/a)-t))*sXUi@YCc} CX|?1Courier New !r = a*sqrt(t-arcsin((b+d)/a))/sqrt(abs(arcsin((b+d)/a)-t))*sXUiŕ@yϋ׃X˽F?1Courier New !seg (0,-a) to (sqrt(a^2-(b+d)^2),b+d)U88ףXUiŕ@yϋ׃|"$|?1Courier New T!seg (0,-a) to (sqrt(a^2-b^2),-a)XUiŕ@yϋ׃eN6?1Courier New ! (x,y) = (cos(t)*sqrt(arctan((b+a)/sqrt(a^2-b^2))-t)/sqrt(absXUiŕ@ ?dv~?1Courier New @@@h!@